How to Square a Trinomial
Squaring a trinomial involves multiplying the trinomial by itself. The process follows the general pattern of the distributive property and is often used in algebraic manipulations or solving mathematical equations. To square a trinomial in the form (ax2 + bx + c), you would multiply it by itself using the distributive property and then simplify the resulting expression.
For example squaring the trinomial (x2 + 2x + 3)
= (x2 + 2x + 3)2
Using Distributive Property:
= (x2 + 2x + 3)(x2 + 2x + 3)
= x2(x2 + 2x + 3) + 2x(x2 + 2x + 3) + 3(x2 + 2x + 3)
= x4 + 2x3 + 3x2 + 2x3 + 4x2 + 6x + 3x2 + 6x + 9
Simplifying and combining like terms,
= x4 + 4x3 + 10x2 + 12x + 9
This process can be applied to any trinomial by following the same steps of multiplying each term in the trinomial by every term in the trinomial and then simplifying the result.
We can also use the Squaring a Trinomial Formula to find the square of a trinomial.
Squaring a Trinomial Formula
Squaring a Trinomial Formula is,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
Also,
(ax2 + bx + c)2 = a2x4 + 2abx3 + (2ac + b2)x2 + 2bcx + c2
Must Read
Squaring a Trinomial
Squaring a trinomial involves multiplying a trinomial by itself. A trinomial is an algebraic expression with three terms, typically of the form a+b+c where a, b, and c represent constants or variables.
It requires multiplying the trinomial by itself using the distributive property and then simplifying the expression by combining like terms. This process is fundamental in algebra and provides an expanded form of the trinomial.
Let’s know more Trinomial Definition, How to Square Trinomial, and Different Methods of Squaring a Trinomial with some solved examples to understand better.